A space-borne clock calibration method and apparatus

Abstract

The application provides a kind of on-board clock calibration method and device, which can be applied to spacecraft time-frequency system technical field.The method comprises: based on the orbit state information of the spacecraft to which the target on-board clock belongs, the orbit type of the spacecraft is determined, wherein the orbit type comprises at least one of the geocentric orbit, the selenocentric orbit and the distant retrograde orbit;According to the orbit type, the frequency difference analytical equation of the target on-board clock relative to the time of the earth is obtained, and the frequency difference analytical equation contains the long-term item model and the periodic item model of frequency difference;The integral operation is carried out on the frequency difference analytical equation, and the time difference analytical equation of the target on-board clock relative to the time of the earth is obtained;Based on the time difference analytical equation, the clock error compensation is carried out on the target on-board clock.

Description

Technical Field

[0001] This application relates to the field of spacecraft time and frequency system technology, and more specifically to a method and apparatus for calibrating a spaceborne clock. Background Technology

[0002] Satellite navigation, deep space exploration, and space-to-ground time synchronization all rely on highly stable onboard clocks (or satellite clocks). The stability of the satellite clock's output frequency and the accuracy of its accumulated clock bias directly affect positioning, navigation, and timing performance.

[0003] In related technologies, relativistic frequency shift modeling methods for star clocks can be mainly divided into two categories: one is represented by global satellite navigation systems, which, based on the geocentric two-body orbit assumption, expresses the frequency shift of the star clock relative to the ground reference time as a combination of gravitational redshift and second-order Doppler terms, and is suitable for simplified frequency shift correction of medium and high orbit satellites; the other uses high-precision orbit recursion and numerical integration to calculate gravitational potential, velocity and perturbation terms epoch by epoch and obtain the clock difference of the star clock relative to the reference time through time integration. For near-lunar and Earth-Moon space application scenarios, the lunar gravitational field, solar tidal perturbation terms and Earth-Moon three-body dynamics model can also be introduced to improve the accuracy of time-frequency deviation calculation. Although the above methods can realize star clock relativistic frequency shift modeling in specific application scenarios, there are still obvious limitations: (1) In complex gravitational environments such as near-Earth, near-Moon and Earth-Moon space, the applicability of traditional geocentric two-body simplified models is significantly reduced; (2) Methods that rely on high-fidelity numerical integration require continuous input of high-precision ephemeris and complex dynamic models, resulting in large computational load and insufficient real-time performance; (3) Existing models mostly output epoch-by-epoch original frequency difference sequences, lacking a structured description of time-frequency characteristics, making it difficult to support efficient engineering applications; (4) For long-distance retrograde orbits, existing technologies cannot quickly construct analytical or semi-analytical time-frequency prediction expressions for long-term future periods based solely on instantaneous states.

[0004] Therefore, in order to solve the problems of limited modeling accuracy, insufficient real-time computation, and difficulties in engineering application in complex scenarios such as near-Earth, near-Moon, and distant retrograde orbits, there is an urgent need for a spaceborne clock calibration scheme that combines analytical resolution, feasibility, and engineering applicability within the Earth time reference frame. Summary of the Invention

[0005] In view of the above problems, embodiments of this application provide a method and apparatus for calibrating a spaceborne clock.

[0006] According to a first aspect of this application, a method for calibrating a spaceborne clock is provided, comprising: determining the orbital type of the spacecraft based on the orbital state information of the spacecraft to which the target spaceborne clock belongs, wherein the orbital type includes at least one of geocentric orbit, lunar orbit, and distant retrograde orbit; obtaining an analytical equation for the frequency difference of the target spaceborne clock relative to Earth time based on the orbital type, the analytical equation for the frequency difference including a long-term frequency difference model and a periodic frequency difference model, wherein the long-term frequency difference model is used to characterize the cumulative deviation of the spaceborne clock frequency over time, and the periodic frequency difference model is used to characterize the periodic fluctuation deviation of the spaceborne clock frequency; performing an integral operation on the analytical equation for the frequency difference to obtain an analytical equation for the time difference of the target spaceborne clock relative to Earth time; and performing clock error compensation on the target spaceborne clock based on the analytical equation for the time difference.

[0007] According to an embodiment of this application, in response to determining that the spacecraft's orbit type is a long-distance retrograde orbit, the analytical equation for the frequency difference of the target satellite clock relative to Earth time is obtained based on the orbit type, including: acquiring the single-point state corresponding to a preset time on the long-distance retrograde orbit, the single-point state including a position vector and a velocity vector; acquiring time-series state data within a preset time period based on the single-point state, wherein the time-series state data includes position vectors and velocity vectors corresponding to multiple sampling times arranged in chronological order; determining the Jacobian constant for each sampling time based on the time-series state data, and calculating the average value of the Jacobian constant within the preset time period; determining the standard orbit corresponding to the spacecraft under the circularly restricted three-body problem based on the average value of the Jacobian constant, and acquiring standard time-series state data within the preset orbital period; fitting harmonic coefficients of the velocity in the Earth-center distance, Moon-center distance, and Earth-Moon mass center reference frame based on the standard time-series state data, respectively, to obtain multiple corresponding fitting models; and determining the analytical equation for the frequency difference of the target satellite clock relative to Earth time based on the fitting models.

[0008] According to an embodiment of this application, the method further includes: superimposing a solar tidal compensation term into the frequency difference analytical equation to obtain a modified frequency difference analytical equation, wherein the solar tidal compensation term comprises a long-term constant frequency difference term and a frequency difference periodic term of the synodic lunar angular frequency.

[0009] According to an embodiment of this application, in response to determining that the orbit type of the spacecraft is a geocentric orbit or a lunar orbit, the frequency difference analytical equation of the target satellite clock relative to Earth time is obtained based on the orbit type, including: obtaining the orbital elements of the spacecraft in the centroid reference frame corresponding to the orbit type; decomposing the long-term frequency difference model and the periodic frequency difference model based on the orbital elements and the relativistic frequency shift relationship between the coordinate time of different centroid reference frames and Earth time; and combining the long-term frequency difference model and the periodic frequency difference model to obtain the frequency difference analytical equation of the target satellite clock relative to Earth time.

[0010] According to an embodiment of this application, in response to determining that the spacecraft's orbit type is a lunar orbit, the long-term frequency difference model is obtained as follows: based on the orbital elements, a first long-term frequency difference term is determined, generated by aligning the target spacecraft's onboard clock's inherent time with the local lunar coordinates. This first long-term frequency difference term characterizes the combined time delay effect of the second-order Doppler shift and the lunar non-spherical gravitational field on the spacecraft. Based on the Earth-Moon average distance and the Earth-Moon gravitational potential difference, a second long-term frequency difference term is determined, generated by aligning the lunar local coordinates with the Earth's center of mass coordinates. This second long-term frequency difference term characterizes the Earth's orbital characteristics. Frequency shift caused by the combined effect of the Earth-Moon gravitational potential energy difference and velocity difference in the lunar system; the third long-term frequency difference term resulting from the alignment of Earth's center of mass coordinates with Earth time is obtained, and the third long-term frequency difference term is used to characterize the fixed reference shift between Earth's center of mass coordinates and Earth time; based on the average distance from the Sun to the Earth-Moon center of mass and the difference in Earth-Moon gravitational potential, the long-term solar tidal frequency difference term caused by solar tidal perturbation is obtained; the first, second, and third long-term frequency difference terms and the long-term solar tidal frequency difference term are combined to obtain the long-term frequency difference term model of the target satellite clock.

[0011] According to an embodiment of this application, in response to determining that the spacecraft's orbit type is a lunar orbit, the frequency difference periodic term model is obtained as follows: Based on the orbital elements, a general relativistic gravitational time delay model is obtained, and the first long-term frequency difference term is removed to separate the first frequency difference periodic term generated by aligning the target spacecraft's onboard clock with the local lunar coordinates; Based on the Earth-Moon gravitational potential difference and the lunar orbital elements, an Earth-Moon time frequency difference model is obtained, and the second long-term frequency difference term is removed to determine the second frequency difference periodic term generated by aligning the lunar local coordinates with the Earth's center of mass coordinates; The third frequency difference term generated by aligning the Earth's center of mass coordinates with Earth time is obtained. The periodic term, specifically the third frequency difference periodic term, is used to characterize the periodic fluctuation deviation between Earth's center-of-mass coordinates and Earth time. Based on the motion state vector of the Moon's center in the Earth-Moon center-of-mass reference frame and the motion state vector of the spacecraft in the Moon's center reference frame, the non-inertial reference frame transformation coupling term is determined. Based on the gravitational parameters of the Sun, Earth, and Moon, the solar tidal torque model is obtained, and the long-term solar tidal frequency difference term is removed to separate the solar tidal frequency difference periodic term. The frequency difference periodic term model of the target satellite clock is determined by combining the first, second, and third frequency difference periodic terms, the non-inertial reference frame transformation coupling term, and the solar tidal frequency difference periodic term.

[0012] According to an embodiment of this application, in response to determining that the spacecraft's orbit type is a geocentric orbit, the long-term frequency difference model is obtained as follows: based on the orbital elements, a fourth long-term frequency difference term is determined, generated by aligning the target satellite clock's inherent time with the Earth's center of mass coordinates. This fourth long-term frequency difference term characterizes the combined time delay effect of the second-order Doppler shift and the Earth's non-spherical gravitational field on the spacecraft. A fifth long-term frequency difference term is obtained, generated by aligning the Earth's center of mass coordinates with Earth time. This fifth long-term frequency difference term characterizes the fixed reference offset between the Earth's center of mass coordinates and Earth time. The fourth and fifth long-term frequency difference terms are combined to obtain the long-term frequency difference model of the target satellite clock.

[0013] According to an embodiment of this application, in response to determining that the spacecraft's orbit type is a geocentric orbit, the frequency difference periodic term model is obtained as follows: Based on the orbital elements, a general relativistic gravitational time delay model is obtained, and the fourth frequency difference long term is removed to separate the fourth frequency difference periodic term generated by aligning the inherent time of the target satellite clock with the Earth's center of mass coordinates. The general relativistic gravitational time delay model is used to characterize the combined time delay effect of gravitational potential, velocity, and the Earth's non-spherical gravitational field on the spacecraft. The fifth frequency difference periodic term generated by aligning the Earth's center of mass coordinates with Earth time is obtained. The fifth frequency difference periodic term is used to characterize the periodic fluctuation deviation between the Earth's center of mass coordinates and Earth time. The fourth and fifth frequency difference periodic terms are combined to obtain the frequency difference periodic term model of the target satellite clock.

[0014] According to an embodiment of this application, the orbital elements used in the frequency difference periodic term model are obtained as instantaneous orbital elements.

[0015] According to a second aspect of this application, a spaceborne clock calibration device is provided, comprising: an orbit type determination module, configured to determine the orbit type of the spacecraft based on the orbital state information of the spacecraft to which the target spaceborne clock belongs, wherein the orbit type includes at least one of geocentric orbit, lunar orbit, and distant retrograde orbit; a frequency difference analytical equation determination module, configured to obtain the frequency difference analytical equation of the target spaceborne clock relative to Earth time according to the orbit type, the frequency difference analytical equation including a long-term frequency difference model and a periodic frequency difference model, wherein the long-term frequency difference model is used to characterize the cumulative deviation of the spaceborne clock frequency over time, and the periodic frequency difference model is used to characterize the periodic fluctuation deviation of the spaceborne clock frequency; a time difference analytical equation determination module, configured to perform an integral operation on the frequency difference analytical equation to obtain the time difference analytical equation of the target spaceborne clock relative to Earth time; and a clock difference compensation module, configured to perform clock difference compensation on the target spaceborne clock based on the time difference analytical equation.

[0016] According to a third aspect of this application, an electronic device is provided, comprising: one or more processors; and a memory for storing one or more computer programs, wherein the one or more processors execute the one or more computer programs to implement the steps of the method described above.

[0017] According to a fourth aspect of this application, a computer-readable storage medium is also provided, on which a computer program or instructions are stored, wherein the computer program or instructions, when executed by a processor, implement the steps of the above-described method.

[0018] According to a fifth aspect of this application, a computer program product is also provided, including a computer program or instructions that, when executed by a processor, implement the steps of the above-described method. Attached Figure Description

[0019] The above-mentioned contents, other objects, features and advantages of this application will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0020] Figure 1 The illustration shows an application scenario of the spaceborne clock calibration method and apparatus according to embodiments of this application;

[0021] Figure 2 A flowchart illustrating a spaceborne clock calibration method according to an embodiment of this application is shown schematically.

[0022] Figure 3 The diagram illustrates a reference frame for the Earth's center of mass, the Earth-Moon center of mass, and the Moon's center of mass according to an embodiment of this application.

[0023] Figure 4 A flowchart illustrating the determination of the analytical equation for the frequency difference of a long-distance retrograde trajectory according to an embodiment of this application is shown schematically.

[0024] Figure 5 Another flowchart illustrating a satellite clock calibration method according to an embodiment of this application is shown schematically;

[0025] Figure 6 A schematic diagram illustrating the structure of a spaceborne clock calibration device according to an embodiment of this application is shown.

[0026] Figure 7 A block diagram schematically illustrates an electronic device suitable for implementing a spaceborne clock calibration method according to an embodiment of this application. Detailed Implementation

[0027] The embodiments of this application will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of this application. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of this application for ease of explanation. However, it will be apparent that one or more embodiments may be implemented without these specific details. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0028] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0029] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0030] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0031] Figure 1 The illustration schematically depicts an application scenario of the spaceborne clock calibration method and apparatus according to embodiments of this application. For example... Figure 1 As shown, the application scenario 100 according to the embodiments of this application may include a spacecraft 101 and a terminal device 102.

[0032] Spacecraft 101 can be a satellite, space station, deep space probe, or any other space platform carrying an onboard clock. This onboard clock, along with other high-precision clock sources, provides a time reference and frequency reference for various payload devices on the spacecraft. Due to the influence of the space environment (such as temperature variations, radiation effects, and relativistic effects), the onboard clock will experience frequency drift and timing errors during long-term operation. Therefore, it needs to be calibrated periodically to ensure time synchronization accuracy.

[0033] Terminal device 102 can be a control terminal or processing terminal with functions of data reception, calculation and analysis, and calibration command issuance. In some embodiments, terminal device 102 can be integrated inside spacecraft 101 as part of onboard real-time control unit; in other embodiments, terminal device 102 can also be deployed independently at ground telemetry and control station to interact with spacecraft 101 through telemetry and control communication link.

[0034] During actual operation, spacecraft 101 continuously collects its own onboard clock timing data, combines it with related information such as on-orbit orbital elements and space environment disturbance parameters, and transmits various raw clock data and on-orbit status data to terminal device 102 in real time via a wireless telemetry and control link. Terminal device 102 performs error calculation, frequency difference correction calculation, and clock deviation quantification analysis on the received raw onboard clock data to accurately determine the frequency deviation of the onboard clock, and then generates clock calibration parameters and calibration control commands adapted to the on-orbit operating conditions, which are then sent back to spacecraft 101. Based on the calibration commands transmitted back by terminal device 102, spacecraft 101 completes a series of calibration operations such as onboard clock frequency adjustment, timing alignment, and deviation compensation, ultimately achieving high-precision synchronous calibration of the onboard clock, ensuring a unified time reference and accurate and reliable timing data throughout the entire on-orbit cycle of the spacecraft.

[0035] It should be noted that the satellite clock calibration method provided in this application embodiment can generally be executed by the terminal device 102. Accordingly, the satellite clock calibration device provided in this application embodiment can generally be installed in the terminal device 102.

[0036] It should be understood that Figure 1 The number of spacecraft and terminal equipment shown is merely illustrative. Depending on the implementation requirements, any number of spacecraft and terminal equipment can be included.

[0037] Figure 2 A flowchart illustrating a spaceborne clock calibration method according to an embodiment of this application is shown schematically. Figure 2 As shown, the spaceborne clock calibration method 200 according to an embodiment of this application may include steps S210 to S230.

[0038] In step S210, the orbital type of the spacecraft is determined based on the orbital state information of the spacecraft to which the target satellite's onboard clock belongs. The orbital type includes at least one of the following: geocentric orbit, lunar orbit, and long-distance retrograde orbit.

[0039] In the embodiments of this application, orbital state information is a set of parameters used to uniquely and completely describe the spacecraft’s spatial position and motion state at a certain moment, which can be represented by orbital elements or position and velocity vectors.

[0040] A geocentric orbit is an orbit with the Earth's center of mass or gravitational center as its focus. Low Earth Orbit (LEO) is a type of geocentric orbit, which refers to an orbit around the Earth at an altitude of approximately 160 to 2000 kilometers above the Earth's surface.

[0041] A lunar orbit is an orbit with the Moon's center of mass as its gravitational center or focus. A low lunar orbit (LLO) is a type of lunar orbit, which refers to a low-altitude orbit in which a spacecraft orbits the Moon, generally at an altitude of about 10 to 100 kilometers above the lunar surface.

[0042] Distant Retrograde Orbit (DRO) is a type of large-scale three-body dynamic periodic orbit in the Earth-Moon space that recurs around the Moon in retrograde motion and around the Earth in prograde motion.

[0043] For example, the acquired orbital state information of a spacecraft can be orbital elements, including the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, and true anomaly. For a geocentric orbit, the criteria are: the central celestial body is Earth, and the perigee altitude calculated from the semi-major axis and eccentricity is less than 2000 km (e.g., a semi-major axis of approximately 6878 km, an eccentricity of approximately 0.001, corresponding to a circular orbit at an altitude of approximately 500 km). For a lunar-centric orbit, the criteria are: the central celestial body is the Moon, and the orbital altitude is relatively low (e.g., a semi-major axis of approximately 1838 km, an eccentricity of approximately 0.001, corresponding to a circular orbit around the Moon at an altitude of approximately 100 km). For a distant retrograde orbit, the criteria are: the central celestial body is the Moon, the orbital altitude is much higher than that of a lunar-centric orbit (e.g., a semi-major axis of approximately 50000 km), and the orbital inclination is close to 180 degrees (retrograde characteristics, e.g., an inclination of 178 degrees). By extracting the central celestial body identifier, semi-major axis, eccentricity, and orbital inclination from the orbital elements and comparing them with the aforementioned characteristic parameter thresholds, the orbital type of the spacecraft can be uniquely determined.

[0044] In step S220, based on the orbit type, the analytical equation for the frequency difference of the target satellite clock relative to Earth time is obtained. The analytical equation for the frequency difference includes a long-term frequency difference model and a periodic frequency difference model. The long-term frequency difference model is used to characterize the cumulative deviation of the satellite clock frequency over time, and the periodic frequency difference model is used to characterize the periodic fluctuation deviation of the satellite clock frequency.

[0045] Terrestrial Time (TT) is a continuously used time scale for high-precision time comparison and theoretical modeling in the vicinity of Earth. Aligning onboard clocks with TT not only provides a unified reference for time conversion between space and ground systems, maintaining satellite time standards, and high-precision time synchronization, but also improves the compatibility and scalability of navigation and timing systems for different users and spacecraft platforms. Specifically, when all onboard clocks within a spacecraft maintain the same frequency as TT, satellites, ground stations, and other user terminals can achieve frequency coordination and time synchronization on the Earth reference time scale, thereby reducing the complexity of time conversion and improving time-frequency consistency during inter-satellite coordination, space-ground coordination, and heterogeneous user access.

[0046] In the embodiments of this application, by analyzing and modeling the perturbation characteristics and evolution law of the frequency difference of the onboard clock as it moves with its orbit, the frequency difference can be explicitly decomposed into two components: a long-term term and a periodic term. Based on this, differentiated models are constructed according to orbit type, establishing corresponding long-term and periodic frequency difference models for each type of orbit, thereby achieving a refined characterization of the evolution law of the onboard clock frequency difference under various orbital conditions.

[0047] Figure 3 A schematic diagram illustrating the Earth's center of mass, the Earth-Moon center of mass, and the Moon's center of mass reference frames according to embodiments of this application is provided. Figure 3 As shown, the Geocentric Celestial Reference System (GCRS) is a coordinate system with the Earth's center of mass as its origin, the Lunar Celestial Reference System (LCRS) is a coordinate system with the Moon's center of mass as its origin, and the Earth-Moon Celestial Reference System (EMCRS) is a coordinate system with the common center of mass of the Earth-Moon system as its origin. The derivation of the time-frequency difference equation for the LEO satellite clock in this application is primarily based on GCRS. The derivation of the time-frequency difference equation for the DRO and LLO satellite clocks involves GCRS, LCRS, and EMCRS.

[0048] For example, if the spacecraft belongs to LEO, then a mapping from LEO to Earth's Geocentric Coordinate Time (TCG) and from TCG to TT is established under GCRS. Based on the mapping relationship, the long-term term model of LEO frequency difference can be obtained using the reference semi-major axis, reference eccentricity and reference inclination, and the periodic term model of LEO frequency difference around the long-term term can be obtained using the instantaneous orbital elements.

[0049] If it belongs to LLO, then establish the mapping from LLO to Lunar Local Coordinate (TCL), TCL to TCG, and TCG to TT. Based on the mapping relationship, the long-term term model of LLO frequency difference can be obtained using the reference semi-major axis, reference eccentricity, and reference tilt. Solar tidal terms can be introduced into this model as needed. For the frequency difference periodic term model of LLO, it can be obtained using instantaneous orbital elements, lunar ephemeris, solar position, and the velocity / acceleration of the moon relative to the Earth-Moon mass center. Solar tidal terms and non-inertial reference frame transformation coupling terms can be introduced into this model as needed.

[0050] If it belongs to DRO, then in the EMCRS or equivalent Earth-Moon centroid dynamics framework, establish a frequency difference model composed of the Earth-Moon space center gravity and fitted harmonic terms; the constant terms in the fitted frequency difference model can be used as long-term terms, and solar tidal long-term compensation can be superimposed when needed; at the same time, the cosine combination of distance and velocity can be fitted using standard orbital sample points, and the harmonic form of DRO frequency difference periodic terms can be generated accordingly.

[0051] In step S230, the frequency difference analytical equation is integrated to obtain the time difference analytical equation of the target satellite clock relative to Earth time.

[0052] In the embodiments of this application, the obtained frequency difference analytical equation is integrated to obtain the time difference analytical equation of the satellite clock relative to TT. The integration method can be analytical integration, piecewise analytical integration, or numerical integration.

[0053] In step S240, clock difference compensation is performed on the target satellite clock based on the time difference analytical equation.

[0054] For example, when the orbit type is a geocentric or lunar orbit, the spacecraft's current orbital elements can be substituted into the constructed time difference analytical equation as input variables to calculate the clock error correction of the target satellite's clock relative to TT at the current moment. When the orbit type is a long-distance retrograde orbit, the time difference analytical equation can first be parameter-fitted based on the historical geocentric distance, lunar distance, and position and velocity vectors in the Earth-Moon inertial frame of the standard orbit. After completing the parameter fitting, the currently measured geocentric distance, lunar distance, and position and velocity vectors in the Earth-Moon inertial frame are substituted into the time difference analytical equation as input variables to calculate the clock error correction at the current moment. The clock error correction includes both long-term cumulative components and periodic fluctuation components. After obtaining the clock error correction, advance or lag compensation can be applied to the target satellite's clock output to suppress clock drift accumulation on long-term timescales and offset relativistic frequency shift fluctuations caused by orbital motion on short-period timescales, ensuring that the target satellite's clock maintains the predetermined synchronization accuracy with Earth time. This has led to the development of an engineering implementation strategy of "long-term pre-adjustment + periodic compensation", which significantly improves the overall time accuracy and system reliability of spacecraft in navigation and positioning, precision timing and multi-platform collaborative missions.

[0055] According to the embodiments of this application, by constructing time difference and frequency difference models that match the orbital dynamics environment, the applicability and modeling accuracy of the models under different orbital scenarios are effectively improved. At the same time, by explicitly decomposing the frequency difference of the spaceborne clock relative to Earth time into long-term and periodic terms, the model output can be more directly converted into spaceborne clock control parameters, thereby significantly enhancing its engineering practical value. In addition, by adopting analytical expressions for long-term and periodic terms and combining them with parametric fitting methods to replace epoch-by-epoch numerical integration, there is no need to continuously perform high-complexity dynamic propagation during the spaceborne clock calibration process. This can significantly reduce the computational burden while reducing the dependence on continuous external high-precision data, further improving the real-time prediction capability and engineering implementation efficiency of the spaceborne clock frequency difference and time difference.

[0056] Figure 4 A flowchart illustrating the determination of the analytical equation for the frequency difference of a long-distance retrograde orbit according to an embodiment of this application is shown schematically. Figure 4 As shown, the method 400 of this embodiment may include steps S410 to S460.

[0057] In step S410, the single-point state corresponding to a preset time on the spacecraft's long-distance retrograde orbit is obtained. The single-point state includes the position vector and the velocity vector.

[0058] In the embodiments of this application, a single-point state refers to a set of parameters that uniquely describes the motion state of a spacecraft at a specific moment, mainly including a position vector and a velocity vector. The position vector is a vector pointing from the origin to the spacecraft's location in a selected inertial coordinate system, used to characterize its geometric position in space; the velocity vector is a vector describing the speed and direction of the spacecraft's motion at that moment, reflecting its instantaneous dynamic characteristics. For example, the single-point state of the spacecraft at a preset moment can be denoted as: Where i represents a specific preset time index. This is the position vector corresponding to that moment. This is the corresponding velocity vector.

[0059] In step S420, based on the single-point state, time-series state data within a preset time period is acquired. This time-series state data includes position and velocity vectors corresponding to multiple sampling times arranged in chronological order.

[0060] In the embodiments of this application, a single point state can be used as the starting point for sampling. Based on the dynamic model of the long-distance retrograde orbit, the orbit extrapolation is performed on the time period. In this way, the position vector and velocity vector of multiple epochs (i.e. sampling time) are extracted within a preset time period according to a specific strategy (such as equal intervals along the time axis), so as to obtain the time-series state data of the spacecraft on the long-distance retrograde orbit.

[0061] For example, a High Precision Orbit Propagator (HPOP) model can be used as the orbit extrapolation model. This is based on a single-point state. Starting from this point, a one-month forecast is made of the spacecraft's motion on a distant retrograde orbit. Within this one-month orbital arc, the instantaneous state at m-1 sampling moments is extracted at equal intervals. For example, if m is 9, the states corresponding to 8 sampling moments will be obtained, compared with the initial... Together they form a set of time-series state data containing 9 states.

[0062] Optionally, time-series status data can be collected based on the historical orbital arc segment of the spacecraft on a long-distance retrograde orbit.

[0063] In step S430, the Jacobian constant at each sampling time is determined based on the time-series state data, and the average value of the Jacobian constant within a preset time period is calculated.

[0064] In the embodiments of this application, the Jacobian constant is the only conserved constant in the Circular Restricted Three-Body Problem (CR3BP). The corresponding Jacobian constant can be calculated for each sampled state; after obtaining the total number of Jacobian constants, the arithmetic mean of the Jacobian constants can be obtained.

[0065] In step S440, based on the Jacobian constant mean, the standard orbit corresponding to the spacecraft under the circularly restricted three-body problem is determined, and the standard time sequence state data within the preset orbital period is obtained.

[0066] In the embodiments of this application, the standard orbit corresponding to the spacecraft under the circularly restricted three-body problem can be determined based on the Jacobian constant mean. Based on this, single-point states are utilized. The phase information can be used to determine the corresponding initial phase on a standard orbit, and from this, the state at that single point can be deduced. Corresponding initial state This enables accurate positioning and identification of the initial state on the standard orbit.

[0067] To obtain sufficiently long time series data, it is possible to start from the initial state. As a starting point, predict two standard orbital periods (i.e.,) under a standard orbit. Subsequently, n-1 discrete state points (e.g., n=20) are extracted from the predicted trajectory according to the preset sampling interval, and this set of time series data is established as the standard time series state data.

[0068] In step S450, based on standard time-series state data, harmonic coefficients are fitted to the velocities in the Earth-center distance, Moon-center distance, and Earth-Moon mass center reference frame, respectively, to obtain multiple corresponding fitting models.

[0069] In the embodiments of this application, the geocentric distance can refer to the straight-line distance from the spacecraft to the Earth's center of mass. The lunar distance can refer to the straight-line distance from the spacecraft to the Moon's center of mass. Based on standard time-series state data, harmonic coefficients can be fitted to the geocentric distance, lunar distance, and velocity components in the Earth-Moon center-of-mass reference frame, thereby obtaining multiple fitting models characterizing the orbital periodicity.

[0070] Specifically, standard time-series state data obtained from forecasts can be used, along with mathematical expressions composed of combinations of cosine functions, to determine the geocentric distance (denoted as ). ), lunar distance (denoted as and velocity in the Earth-Moon barycenter reference frame ( Least square fitting is performed to construct three corresponding harmonic fitting models to accurately describe the periodic variation of these physical quantities over time.

[0071] Specifically, regarding the distance from the Earth's center The harmonic coefficient fitting formula can be expressed as:

[0072] ;

[0073] Where a represents a constant term; Represents the fundamental frequency oscillation term; This represents the secondary frequency oscillation term with phase. The initial phase is determined based on the initial position of the DRO in the Earth-Moon barycentric reference frame; denoted as the second harmonic term; b, c, and d represent the amplitudes of the fundamental frequency oscillation term, the second frequency oscillation term, and the second harmonic term, respectively. , Frequency; frequency The corresponding period is the lunar orbital period; frequency The corresponding period is the DRO lunar orbital period.

[0074] ;

[0075] in, Indicates the moon's orbital period; Indicates the standard orbital period of DRO; Let represent the coordinates in the coordinate system of the circularly restricted three-body problem; Represents lunar coordinates; The coordinates of the spacecraft are represented by M; M is the design matrix composed of the cosine basis functions at each sampling time. Y represents the transpose of M; Y is the corresponding distance or velocity sample vector; X is the vector of fitting coefficients to be determined.

[0076] For lunar distance and velocity in the Earth-Moon barycenter reference frame It can be used with respect to the distance from the Earth's center. The same fitting formula is used for fitting to obtain... , , Three fitting models.

[0077] In step S460, based on the fitted model, the analytical equation for the frequency difference of the target satellite clock relative to Earth time is determined.

[0078] In the embodiments of this application, the frequency difference analytical equation of the target satellite clock relative to Earth time can be obtained by jointly fitting multiple fitting models.

[0079] Specifically, based on , , Three fitting models can be used to calculate the frequency difference in the Earth-Moon barycentric reference frame, retaining only the gravitational potential term up to the center. The relationship between the original time and coordinate time of the term DRO can be expressed as:

[0080] ;

[0081] in, This indicates the time of the onboard clock, i.e., the original time. ; Represents the Earth's gravitational constant; Represents the lunar gravitational constant; This represents the distance from the spacecraft to the Earth's center of mass at coordinate time t; This represents the distance from the spacecraft to the center of mass of the moon at coordinate time t; This represents the spacecraft's coordinate velocity in the Earth-Moon center-of-mass reference frame. The frequency difference analytical equation can then be preserved in cosine combination form:

[0082] ;

[0083] Where A, B, C, and D are frequency difference coefficients obtained by harmonic balance or Fourier truncation based on the reciprocal distance term and the square velocity term. A represents the constant term; B, C, and D are the amplitudes of the corresponding frequency components. The constant term A in this cosine combination form of the frequency difference analytical equation can be used as the long-term frequency difference model, and B, C, and D can be used as the periodic frequency difference model.

[0084] According to the embodiments of this application, by utilizing the quasi-periodic structure of the DRO orbit, the complex three-body motion is compressed into a small number of parameterized coefficients. It is possible to determine the standard orbit and initial phase using a single-point state, and to perform harmonic fitting on the distance from the Earth's center, the distance from the Moon's center, and the velocity, thereby constructing a frequency difference prediction expression. This solves the problem that DRO cannot be stably and analytically described using traditional orbital elements, and overcomes the shortcomings of existing technologies that make it difficult to quickly construct time-frequency prediction expressions for a longer period of time based solely on a single-point state. This effectively improves the autonomous prediction capability and engineering implementation efficiency in the DRO scenario.

[0085] In the embodiments of this application, the spaceborne clock calibration method may further include: superimposing a solar tidal compensation term into the frequency difference analytical equation to obtain a modified frequency difference analytical equation, wherein the solar tidal compensation term comprises a long-term constant frequency difference term and a frequency difference periodic term of the synodic lunar angular frequency.

[0086] Specifically, the corrected frequency difference analytical equation can be expressed as:

[0087] ;

[0088] in, The solar tidal compensation term can be expressed as follows:

[0089] ;

[0090] ;

[0091] ;

[0092] in, This represents the average distance from the Sun to the Earth-Moon barycenter; and This represents the mean square value of the period of the standard DRO reference orbit in the X and Y directions; Indicates the Earth-Moon mass parameter; Indicates the average distance between the Earth and the Moon; It represents the directional phase angle of the Sun relative to the positive direction of the line connecting the Earth and the Moon in the Earth-Moon barycentric reference frame; Indicates the synodic angular frequency of the moon; This represents the initial phase angle.

[0093] Solar tidal compensation item It can be further decomposed into long-term terms and periodic terms. The formula for the long-term term can be expressed as:

[0094] ;

[0095] The formula for the periodic term can be expressed as:

[0096] .

[0097] After superimposing the solar tidal compensation term into the frequency difference analytical equation, A can be compared with... As a long-term frequency deviation model, B, C, D, and As a frequency difference periodic term model.

[0098] Alternatively, when solar tidal compensation is not required, it can be set to... .

[0099] According to embodiments of this application, by introducing and superimposing solar tidal compensation terms into the frequency difference analytical equation, the frequency drift deviation caused by periodic gravitational perturbation can be effectively corrected, thereby significantly improving the accuracy and stability of frequency difference calculation.

[0100] In embodiments of this application, in response to determining that the spacecraft's orbit type is a geocentric orbit or a lunar orbit, obtaining the frequency difference analytical equation of the target satellite clock relative to Earth time based on the orbit type may include: obtaining the orbital elements of the spacecraft in the centroid reference frame corresponding to the orbit type; decomposing the long-term frequency difference model and the periodic frequency difference model based on the orbital elements and the relativistic frequency shift relationship between the coordinate time of different centroid reference frames and Earth time; and combining the long-term frequency difference model and the periodic frequency difference model to obtain the frequency difference analytical equation of the target satellite clock relative to Earth time.

[0101] Specifically, when a spacecraft's orbit is a geocentric orbit or a lunar orbit, orbital elements can be used to characterize the spacecraft's orbit. For LEO, the orbital elements under GCRS can be obtained; for LLO, the orbital elements under LCRS can be obtained. For example, the orbital elements can be the average orbital elements or the instantaneous orbital elements. Based on the orbital elements and the long-term relativistic frequency shift relationship between the coordinate time of different centroid reference frames and Earth time, a long-term frequency difference model can be calculated; based on the orbital elements and the general relativistic gravitational time delay, a periodic frequency difference model can be calculated. Combining the long-term and periodic frequency difference models (e.g., through linear superposition) yields the analytical equation for the frequency difference of the target satellite's clock relative to Earth time.

[0102] According to the embodiments of this application, by using orbital elements, long-term frequency deviation and periodicity models for LEO and LLO scenarios were established respectively, and frequency deviation analytical equations were generated by fusion, which effectively improved the modeling accuracy in near-lunar and Earth-Moon space environments, and at the same time improved the feasibility of converting model parameters into star clock control quantities.

[0103] In the embodiments of this application, in response to determining that the spacecraft's orbit type is a lunar orbit, the long-term frequency difference model is obtained as follows: based on the orbital elements, a first long-term frequency difference term is determined, generated by aligning the target spacecraft's onboard clock's inherent time with the local lunar coordinates. This first long-term frequency difference term characterizes the combined time delay effect of the second-order Doppler shift and the lunar non-spherical gravitational field on the spacecraft. Based on the Earth-Moon average distance and the Earth-Moon gravitational potential difference, a second long-term frequency difference term is determined, generated by aligning the lunar local coordinates with the Earth's center of mass coordinates. This second long-term frequency difference term characterizes the Earth's orbital characteristics. Frequency shift caused by the combined effect of the Earth-Moon gravitational potential energy difference and velocity difference in the lunar system; the third long-term frequency difference term resulting from the alignment of Earth's center of mass coordinates with Earth time is obtained, and the third long-term frequency difference term is used to characterize the fixed reference shift between Earth's center of mass coordinates and Earth time; based on the average distance from the Sun to the Earth-Moon center of mass and the difference in Earth-Moon gravitational potential, the long-term solar tidal frequency difference term caused by solar tidal perturbation is obtained; the first, second, and third long-term frequency difference terms and the long-term solar tidal frequency difference term are combined to obtain the long-term frequency difference term model of the target satellite clock.

[0104] Specifically, for the LLO scenario, the long-term frequency difference model of the target satellite clock consists of multiple sub-terms, including at least the first long-term frequency difference term from LLO to TCL, the second long-term frequency difference term from TCL to TCG, the third long-term frequency difference term from TCG to TT, and the long-term solar tidal term.

[0105] Taking the reference orbital elements as an example, the long-term term model of the frequency difference of the target satellite's onboard clock can be expressed as:

[0106] ;

[0107] in, Indicates the reference semi-major axis of LLO; Indicates the reference tilt angle of the LLO; This represents the average distance between the Earth and the Moon, preferably 384403.9 km; This represents the average distance from the Sun to the Earth-Moon barycenter, preferably taken as 1 AU; This represents the ratio constant between TCG and TT; This represents the first long-term term of the frequency difference between LLO and TCL; This represents the second long-term term of the frequency difference between TCL and TCG. This represents the long-term term of the third frequency difference between TCG and TT; This represents the long-term term of the solar tidal frequency variation.

[0108] The first long-term frequency difference term between LLO and TCL , can be represented as:

[0109] ;

[0110] in, Indicates the reference eccentricity of the LLO; The gravitational constant of the moon; The average radius of the moon; The second-order band harmonic coefficients represent the non-spherical gravitational field of the Moon.

[0111] The second long-term frequency difference term between TCL and TCG , can be represented as:

[0112] ;

[0113] in, is the Earth's gravitational constant.

[0114] The third long-term frequency difference term between TCG and TT , can be represented as:

[0115] ;

[0116] in, It is the ratio constant of TCG to TT.

[0117] Long-term solar tidal frequency variation , can be represented as:

[0118] .

[0119] According to embodiments of this application, by decomposing the long-term frequency difference model of the lunar orbit (LLO) target satellite clock into: a first long-term frequency difference term between LLO and TCL, a second long-term frequency difference term between TCL and TCG, a third long-term frequency difference term between TCG and TT, and a long-term solar tidal frequency difference term, this structure explicitly introduces the effects of Earth-Moon relativistic time conversion and solar tidal perturbation, overcoming the systematic mismatch problem caused by single-scale modeling and significantly improving the calculation accuracy under the real gravitational field near the Moon. Simultaneously, aligning the satellite clock with Earth time can reduce the complexity of cross-system time conversion and improve time-frequency consistency during inter-satellite collaboration, satellite-ground collaboration, and heterogeneous user access.

[0120] In the embodiments of this application, in response to determining that the spacecraft's orbit type is a lunar orbit, the frequency difference periodic term model is obtained as follows: Based on the orbital elements, a general relativistic gravitational time delay model is obtained, and the first long-term frequency difference term is removed to separate the first frequency difference periodic term generated by aligning the target spacecraft's inherent time with the local lunar coordinates; Based on the Earth-Moon gravitational potential difference and the lunar orbital elements, an Earth-Moon time frequency difference model is obtained, and the second long-term frequency difference term is removed to determine the second frequency difference periodic term generated by aligning the lunar local coordinates with the Earth's center of mass coordinates; The third frequency difference term generated by aligning the Earth's center of mass coordinates with Earth time is obtained. The periodic term, specifically the third frequency difference periodic term, is used to characterize the periodic fluctuation deviation between Earth's center-of-mass coordinates and Earth time. Based on the motion state vector of the Moon's center in the Earth-Moon center-of-mass reference frame and the motion state vector of the spacecraft in the Moon's center reference frame, the non-inertial reference frame transformation coupling term is determined. Based on the gravitational parameters of the Sun, Earth, and Moon, the solar tidal torque model is obtained, and the long-term solar tidal frequency difference term is removed to separate the solar tidal frequency difference periodic term. The frequency difference periodic term model of the target satellite clock is determined by combining the first, second, and third frequency difference periodic terms, the non-inertial reference frame transformation coupling term, and the solar tidal frequency difference periodic term.

[0121] Specifically, the LLO periodic term consists of multiple sub-terms, including at least: the first frequency difference periodic term from LLO to TCL, the second frequency difference periodic term from TCL to TCG, the third frequency difference periodic term between TCG and TT, the non-inertial reference frame conversion coupling term, and the solar tidal periodic term.

[0122] The first frequency difference period term from LLO to TCL can be expressed as:

[0123] ;

[0124] in, Indicates the semi-major axis of LLO; This represents the eccentricity of the LLO; Indicates the orbital inclination angle of the LLO; Indicates the near-lunar argument of the LLO; Indicates the true nearest angle of LLO; Indicates the near-point angle of LLO; This represents the long-term frequency deviation model, specifically the first long-term frequency deviation term.

[0125] The second frequency difference period term from TCL to TCG can be expressed as:

[0126] ;

[0127] in, Represents the semi-major axis of the Moon's orbit; Indicates the eccentricity of the lunar orbit; This represents the true anomaly angle of the lunar orbit.

[0128] The third frequency difference period term between TCG and TT can be expressed as:

[0129] ;

[0130] Since TCG and TT are converted according to a fixed proportional constant, there is no periodic term.

[0131] The non-inertial reference frame transformation coupling term can be expressed as:

[0132] ;

[0133] in, This indicates the velocity of the lunar center within the Earth-Moon mass center system; This represents the acceleration of the Moon's center within the Earth-Moon mass center system; Indicates the spacecraft's position in the lunar center-of-mass frame of reference; This indicates the spacecraft's velocity in the lunar center-of-mass frame of reference.

[0134] The solar tidal frequency periodic term can be expressed as:

[0135] ;

[0136] in, This represents the distance from the Sun to the Earth-Moon barycenter; Indicates the distance between the Earth and the Moon; This represents the angle between the Earth-Sun vector and the Earth-Moon vector.

[0137] Furthermore, when the lunar gravitational field model is defined in a fixed lunar principal axis frame, the lunar inertial frame orbital elements are first converted to the lunar fixed frame geometric orbital elements. The right ascension of the lunar equatorial ascending node is used during this conversion. Lunar equatorial inclination And the phase angle W of the prime meridian.

[0138] According to embodiments of this application, the lunar non-spherical gravitational field is strongly correlated with the lunar principal axis direction. By considering the effects of the lunar non-spherical gravitational field, the non-inertial reference frame transformation coupling term, and solar tidal perturbations, a frequency difference periodic term model is fitted. This effectively eliminates the mechanical deviation between the low lunar orbit model and the real lunar gravitational field, improves the consistency between the LLO model and the real lunar gravitational field, and thus significantly improves the modeling accuracy of the frequency difference periodic term. Simultaneously, aligning the onboard clock with Earth time reduces the complexity of cross-system time conversion.

[0139] In the embodiments of this application, in response to determining that the spacecraft's orbit type is a geocentric orbit, the long-term frequency difference model is obtained as follows: based on the orbital elements, the fourth long-term frequency difference term generated by aligning the inherent time of the target satellite clock with the Earth's center of mass coordinates is determined. The fourth long-term frequency difference term is used to characterize the combined time delay effect of the second-order Doppler frequency shift and the Earth's non-spherical gravitational field on the spacecraft; the fifth long-term frequency difference term generated by aligning the Earth's center of mass coordinates with Earth time is obtained. The fifth long-term frequency difference term is used to characterize the fixed reference offset between the Earth's center of mass coordinates and Earth time; the fourth and fifth long-term frequency difference terms are combined to obtain the long-term frequency difference model of the target satellite clock.

[0140] Specifically, taking the reference orbital elements as an example, the long-term frequency deviation model of the target satellite clock in the geocentric orbit can be decomposed into two parts: LEO alignment to TCG and TCG alignment to TT. This can be expressed by the formula:

[0141]

[0142] in, A long-term term model representing the frequency difference of the target satellite's onboard clock in a geocentric orbit; The fourth frequency difference long-term term represents the result of aligning the target satellite's clock with the Earth's center of mass coordinates. The fifth frequency difference long-term term resulting from the alignment of Earth's center-of-mass coordinates with Earth time; Indicates the reference semi-major axis of LEO; Indicates the reference eccentricity of LEO; This indicates the reference orbital inclination of LEO. Optionally, if the LEO ephemeris is given, the ephemeris reference parameter is used, and subsequent superscript parameters have the same meaning.

[0143] The fourth frequency difference long-term term resulting from the alignment of the target satellite's clock with the Earth's center of mass coordinates Aligning LEO with TCG can be represented as:

[0144] ;

[0145] in, This represents the second-order band harmonic coefficients of the Earth's non-spherical gravitational field.

[0146] The fifth frequency difference long-term term resulting from the alignment of Earth's center-of-mass coordinates to Earth time That is, TCG aligning with TT can be represented as:

[0147] ;

[0148] in, It is the ratio constant of TCG to TT.

[0149] According to the embodiments of this application, by obtaining the long-term term model of the frequency difference of the geocentric orbit based on the long-term term aligned with the coordinates of the low-orbit satellite to the Earth's center of mass and the long-term term aligned with the Earth's center of mass coordinates to Earth time, the modeling accuracy of the long-term term of the frequency difference of the geocentric orbit can be improved.

[0150] In the embodiments of this application, in response to determining that the spacecraft's orbit type is a geocentric orbit, the frequency difference periodic term model is obtained as follows: Based on the orbital elements, a general relativistic gravitational time delay model is obtained, and the fourth frequency difference long term is removed to separate the fourth frequency difference periodic term generated by aligning the inherent time of the target satellite clock with the Earth's center of mass coordinates. The general relativistic gravitational time delay model is used to characterize the combined time delay effect of gravitational potential, velocity, and the Earth's non-spherical gravitational field on the spacecraft. The fifth frequency difference periodic term generated by aligning the Earth's center of mass coordinates with Earth time is obtained. The fifth frequency difference periodic term is used to characterize the periodic fluctuation deviation between the Earth's center of mass coordinates and Earth time. The fourth and fifth frequency difference periodic terms are combined to obtain the frequency difference periodic term model of the target satellite clock.

[0151] Specifically, the frequency difference periodicity model of the satellite-borne clock in the geocentric orbit target can be expressed as:

[0152] ;

[0153] in, Indicates the semi-major axis of LEO; This indicates the eccentricity of LEO; Indicates the orbital inclination angle of LEO; Indicates the perigee argument of LEO; Indicates the true anterior angle of LEO; Indicates the near-angle of LEO; The fourth frequency difference periodic term represents the result of aligning the target satellite's clock with the Earth's center of mass coordinates. The fifth frequency difference periodic term represents the result of aligning the Earth's center of mass coordinates to Earth time.

[0154] The fourth frequency difference periodic term resulting from the alignment of the target satellite's clock with the Earth's center of mass coordinates , can be represented as:

[0155] ;

[0156] The fifth frequency difference periodic term resulting from aligning the Earth's center-of-mass coordinates to Earth time can be expressed as:

[0157] ;

[0158] Because TCG and TT are proportional constant The transformation means that there are no periodic terms.

[0159] According to the embodiments of this application, the dominant component of the LEO frequency difference is determined by the central gravity and the second-order band harmonic coefficient. By constructing a periodic fitting model that considers the non-spherical gravitational field of the Earth, the modeling accuracy of the frequency difference periodic term can be effectively improved.

[0160] In the embodiments of this application, the orbital elements used to obtain the frequency difference periodic term model are instantaneous orbital elements.

[0161] Instantaneous orbital elements can reflect the motion state of a spacecraft under perturbation in real time, and can more accurately describe the orbital evolution pattern in a short period of time compared with the average orbital elements. Therefore, using instantaneous orbital elements to construct a frequency difference periodic term model can more realistically reflect the periodic characteristics of the signal caused by changes in orbital geometry during propagation, thereby improving the model's fitting accuracy to actual observation data and its adaptability to dynamic environments.

[0162] It should be noted that the frequency difference is uniformly defined in the embodiments of this application as:

[0163] ;

[0164] in, This represents the total deviation of the spacecraft's frequency from the reference frequency; Indicates the spacecraft frequency; This represents the reference frequency. If the opposite definition is used in a specific implementation, the entire frequency difference expression will change sign, but this will not change the technical essence of this application.

[0165] It should be noted that the reference orbital parameters of LEO / LLO are not limited to a specific source and can come from broadcast ephemeris, precise orbit determination results, filtered and smoothed results, autonomous orbit prediction results, or equivalent data; the long-term term can be calculated using the average root number, mean root number, or reference root number, and the periodic term can be calculated using the instantaneous root number, oscillatory root number, or equivalent orbital parameters derived from position and velocity.

[0166] The non-spherical gravity correction in the LEO / LLO model is not limited to the specific truncation form in the embodiments. In practical applications, only the J2 term can be retained, or J3, J4 and other low-order dominant spherical harmonic terms can be introduced, or the relevant terms can be equivalently merged, approximately replaced or segmented.

[0167] The implementation of coordinate system transformation and additional correction terms in the LLO scenario is not limited. The transformation from the lunar inertial frame to the lunar fixed frame can be performed by analytical geometric transformation using lunar libration parameters, or by inversely calculating orbital parameters after numerical coordinate transformation. The time scale transformation from TCL to TCG, solar tidal terms, and non-inertial reference frame transformation coupling terms can be written into the main model or added as independent compensation terms.

[0168] The method for determining the standard orbit and the form of fitting for DRO are not limited. The standard orbit can be selected based on the Jacobian constant, resonance ratio, orbital energy, period, orbital family number, or minimum residual criterion; the fitting object can be the geocentric distance, lunar distance, velocity and their combinations, or their reciprocals, square terms, or other equivalent physical quantities; the fitting basis functions can be cosine combinations, Fourier truncation, mixed sine and cosine basis functions, or other parametric expansion forms.

[0169] The output format and deployment method of the embodiments of this application are not limited. It can output only the long term for preset frequency modulation, or output both the long term and the periodic term for periodic compensation. It can also be combined with a clock bias zeroing strategy with fixed or adaptive intervals to implement control. It can be deployed at the space-based end, at the ground end, or in a space-ground cooperative manner.

[0170] Figure 5 Another flowchart illustrating a satellite clock calibration method according to an embodiment of this application is shown schematically.

[0171] To address the issue that traditional simplified geocentric two-body models are difficult to apply to different orbital scenarios such as LEO, LLO, and DRO, embodiments of this application construct time-frequency difference models that match the orbital dynamics environment. For example... Figure 5As shown, firstly, the orbital type of the spacecraft is determined based on its orbital state information. Then, classification processing is performed according to the orbital type: if the orbital type is geocentric orbit (LEO) or lunar orbit (LLO), the orbital elements of the spacecraft containing the onboard clock in the corresponding celestial body's center of mass frame are obtained. Next, based on the orbital elements, the long-term frequency difference model and the periodic frequency difference model are modeled separately. During the modeling process, the J2 dominant term is introduced into the analytical expression of the model, and techniques such as selecting the square root and processing the lunar fixed-line elements are combined to ensure that the model retains the dominant influence of non-spherical gravity while maintaining a closed or quasi-closed expression. Then, the long-term frequency difference model and the periodic frequency difference model are combined to obtain the analytical equation for the frequency difference of the onboard clock relative to Earth time. Then, the analytical equation for the frequency difference is integrated to obtain the analytical equation for the time difference of the onboard clock relative to Earth time. Finally, clock error compensation is performed on the onboard clock based on the fitting parameters of the analytical equation for the time difference.

[0172] If the orbit type is a long-distance retrograde orbit, firstly, the single-point state of the spacecraft at any time in the long-distance retrograde orbit is obtained; then, using this point as the sampling starting point, the state of a preset number of sampling points is obtained, and the mean value of the Jacobian constant is calculated based on the above state data, and then the standard orbit is determined based on the mean value of the Jacobian constant; then, several sampling points are selected on the standard orbit to obtain the corresponding standard state; then, using the obtained standard state, the harmonic coefficients of the distance from the Earth's center, the distance from the Moon's center, and the velocity in the Earth-Moon mass center reference frame are fitted, thereby obtaining three corresponding fitting models; then, the above fitting models are substituted into the frequency difference calculation formula to obtain the analytical equation of the frequency difference of the spacecraft clock relative to Earth time; then, the analytical equation of the frequency difference is integrated to obtain the analytical equation of the time difference of the spacecraft clock relative to Earth time; then, the clock error compensation of the spacecraft clock is performed based on the fitting parameters of the time difference analytical equation.

[0173] For example, to verify the onboard clock calibration method in the LLO scenario, the simulation time can be set to one year, and the simulation step size can be 60 seconds; the orbital elements can be: semi-major axis 1937.4 km, eccentricity 0.01, inclination 90°, perigee argument 0°, right ascension of ascending node 0°, and true anomaly 0°; the orbital recursive model can adopt HPOP, a 70×70 order lunar gravity field, and Earth's central gravity. When only the long-term term is adjusted, the cumulative clock error over one year is better than 1 μs; when both the long-term and periodic terms are adjusted, the cumulative clock error over one year is better than 0.4 ns.

[0174] For example, to verify the onboard clock calibration method in the DRO scenario, the simulation time can be set to one year, and the simulation step size can be 60 seconds; the initial state of 2:1 DRO is [116545,233788,129454] km and [-1.33416,0.507505,0.227004] km / s, and the initial state of 3:1 DRO (long-distance retrograde orbit) is [124723,250221,138472] km and [-1.33687,0.513617,0.229507] km / s; the orbit recursive model adopts Astrogator cislunar, and the frequency difference calculation model adopts... Cut-off and Earth-Moon central gravity. When adjusting only the long term, the cumulative clock error per year is better than 4 μs; when adjusting both the long term and the periodic term, the cumulative clock error per year is better than 3 μs, and within three months it is better than 1 μs.

[0175] It should be noted that the spaceborne clock calibration method in this application is applicable to all single-center orbits centered on Earth- or Moon-centered celestial bodies. LEO and LLO orbits are used in the specific examples because, under the two-body assumption, the calculation of these two types of orbits is relatively more difficult. Furthermore, the method is not limited to low Earth orbits; it is also applicable to medium Earth orbits and high Earth orbits.

[0176] Based on the above-described spaceborne clock calibration method, embodiments of this application also provide a spaceborne clock calibration device. The following will be combined with... Figure 6 The device is described in detail.

[0177] Figure 6 A schematic block diagram of a spaceborne clock calibration device according to an embodiment of this application is shown.

[0178] like Figure 6 As shown, the onboard clock calibration device 600 in this embodiment includes an orbit type determination module 610, a frequency difference analytical equation determination module 620, a time difference analytical equation determination module 630, and a clock difference compensation module 640.

[0179] The orbit type determination module 610 is used to determine the orbit type of the spacecraft based on the orbital state information of the spacecraft to which the target satellite's onboard clock belongs. The orbit type includes at least one of a geocentric orbit, a lunar orbit, and a distant retrograde orbit. In one embodiment, the orbit type determination module 610 can be used to execute step S210 described above, which will not be repeated here.

[0180] The frequency difference analytical equation determination module 620 is used to obtain the frequency difference analytical equation of the target satellite clock relative to Earth time based on the orbit type. The frequency difference analytical equation includes a long-term frequency difference model and a periodic frequency difference model. The long-term frequency difference model is used to characterize the cumulative deviation of the satellite clock frequency over time, and the periodic frequency difference model is used to characterize the periodic fluctuation deviation of the satellite clock frequency. In one embodiment, the frequency difference analytical equation determination module 620 can be used to perform step S220 described above, which will not be repeated here.

[0181] The time difference analytical equation determination module 630 is used to perform integration on the frequency difference analytical equation to obtain the time difference analytical equation of the target satellite clock relative to Earth time. In one embodiment, the time difference analytical equation determination module 630 can be used to execute step S230 described above, which will not be repeated here.

[0182] The clock error compensation module 640 is used to perform clock error compensation on the target satellite clock based on the time difference analytical equation. In one embodiment, the clock error compensation module 640 can be used to perform step S240 described above, which will not be repeated here.

[0183] According to embodiments of this application, the onboard clock calibration device 600 may include: a remote retrograde orbit frequency difference module and a geocentric / lunar orbit frequency difference module.

[0184] The long-distance retrograde orbit frequency difference module is used to acquire the single-point state of the spacecraft at a preset time on the long-distance retrograde orbit. The single-point state includes position and velocity vectors. Based on the single-point state, it acquires the time-series state data within a preset time period, which includes position and velocity vectors corresponding to multiple sampling times arranged in chronological order. Based on the time-series state data, it determines the Jacobian constant for each sampling time and calculates the average value of the Jacobian constant within the preset time period. Based on the average value of the Jacobian constant, it determines the standard orbit corresponding to the spacecraft under the circularly restricted three-body problem and acquires the standard time-series state data within the preset orbital period. Based on the standard time-series state data, it performs harmonic coefficient fitting on the velocities in the Earth-center distance, Moon-center distance, and Earth-Moon mass center reference frame, respectively, to obtain multiple corresponding fitting models. Based on the fitting models, it determines the analytical equation for the frequency difference of the target spacecraft's onboard clock relative to Earth time.

[0185] The remote retrograde orbit frequency difference module is also used to superimpose solar tidal compensation terms into the frequency difference analytical equation to obtain a modified frequency difference analytical equation. The solar tidal compensation terms consist of a long-term constant frequency difference term and a frequency difference periodic term of the synodic lunar angular frequency.

[0186] The geocentric / lunar orbit frequency difference module is used to obtain the orbital elements of the spacecraft in the centroid reference frame corresponding to the orbital type. Based on the orbital elements and the relativistic frequency shift relationship between the coordinate time of different centroid reference frames and Earth time, the long-term frequency difference model and the periodic frequency difference model are decomposed. The long-term frequency difference model and the periodic frequency difference model are combined to obtain the analytical equation of the frequency difference of the target satellite clock relative to Earth time.

[0187] According to embodiments of this application, the near-Earth / lunar orbit frequency difference module further includes a lunar orbit frequency difference long-term term module, a lunar orbit frequency difference periodic term module, a geocentric orbit frequency difference long-term term module, and a geocentric orbit frequency difference periodic term module.

[0188] The lunar orbital frequency difference long-term term module is used to determine the first frequency difference long-term term generated by aligning the target satellite clock's inherent time with the local lunar coordinates based on orbital elements. This first frequency difference long-term term characterizes the combined time delay effect of the second-order Doppler shift and the non-spherical gravitational field of the moon on the spacecraft. Based on the average Earth-Moon distance and the difference in Earth-Moon gravitational potential, the module determines the second frequency difference long-term term generated by aligning the local lunar coordinates with the Earth's center of mass coordinates. This second frequency difference long-term term characterizes the frequency shift caused by the combined effect of the difference in gravitational potential energy and velocity between the Earth and Moon in the Earth-Moon system. The module also obtains the third frequency difference long-term term generated by aligning the Earth's center of mass coordinates with Earth time. This third frequency difference long-term term characterizes the fixed reference shift between the Earth's center of mass coordinates and Earth time. Based on the average distance from the Sun to the Earth-Moon center of mass and the difference in Earth-Moon gravitational potential, the module obtains the solar tidal frequency difference long-term term caused by solar tidal perturbations. Finally, the module combines the first, second, and third frequency difference long-term terms with the solar tidal frequency difference long-term term to obtain the frequency difference long-term term model of the target satellite clock.

[0189] The lunar orbital frequency difference periodicity module, based on orbital elements, derives a general relativistic gravitational time delay model and removes the first long-term frequency difference term to separate the first frequency difference periodicity term generated by aligning the target satellite's onboard clock's proper time with the local lunar coordinates. Based on the Earth-Moon gravitational potential difference and the Moon's geocentric orbital elements, an Earth-Moon time frequency difference model is obtained, and the second long-term frequency difference term is removed to determine the second frequency difference periodicity term generated by aligning the Moon's local coordinates with the Earth's center-of-mass coordinates. Finally, the third frequency difference periodicity term is obtained by aligning the Earth's center-of-mass coordinates with Earth's time, and this third frequency difference periodicity term is used to characterize the Earth. The periodic fluctuation deviation between the center-of-mass coordinates and Earth time is determined; based on the motion state vector of the lunar center in the Earth-Moon center-of-mass reference frame and the motion state vector of the spacecraft in the lunar center reference frame, the non-inertial reference frame transformation coupling term is determined; based on the gravitational parameters of the Sun, Earth, and Moon, the solar tidal torque model is obtained, and the long-term solar tidal frequency difference term is removed to separate the solar tidal frequency difference periodic term; based on the combination of the first frequency difference periodic term, the second frequency difference periodic term, the third frequency difference periodic term, the non-inertial reference frame transformation coupling term, and the solar tidal frequency difference periodic term, the frequency difference periodic term model of the target satellite clock is determined.

[0190] The geocentric orbit frequency difference long-term term module is used to determine the fourth frequency difference long-term term generated by aligning the target satellite clock's inherent time with the Earth's center of mass coordinates based on the orbital elements. The fourth frequency difference long-term term is used to characterize the combined time delay effect of the second-order Doppler frequency shift and the Earth's non-spherical gravitational field on the spacecraft. The module also obtains the fifth frequency difference long-term term generated by aligning the Earth's center of mass coordinates with Earth time. The fifth frequency difference long-term term is used to characterize the fixed reference offset between the Earth's center of mass coordinates and Earth time. The fourth and fifth frequency difference long-term terms are combined to obtain the frequency difference long-term term model of the target satellite clock.

[0191] The geocentric orbital frequency difference periodic term module is used to obtain the general relativistic gravitational time delay model based on the orbital elements, and remove the fourth frequency difference long term to separate the fourth frequency difference periodic term generated by aligning the inherent time of the target satellite clock with the Earth's center of mass coordinates. The general relativistic gravitational time delay model is used to characterize the combined time delay effect of gravitational potential, velocity, and the Earth's non-spherical gravitational field on the spacecraft. The fifth frequency difference periodic term generated by aligning the Earth's center of mass coordinates with Earth time is obtained. The fifth frequency difference periodic term is used to characterize the periodic fluctuation deviation between the Earth's center of mass coordinates and Earth time. The fourth and fifth frequency difference periodic terms are combined to obtain the frequency difference periodic term model of the target satellite clock.

[0192] According to embodiments of this application, any multiple modules among the track type determination module 610, frequency difference analytical equation determination module 620, time difference analytical equation determination module 630, and clock difference compensation module 640 can be combined into one module, or any one of these modules can be split into multiple modules. Alternatively, at least part of the functionality of one or more of these modules can be combined with at least part of the functionality of other modules and implemented in one module. According to embodiments of this application, at least one of the track type determination module 610, frequency difference analytical equation determination module 620, time difference analytical equation determination module 630, and clock difference compensation module 640 can be at least partially implemented as hardware circuitry, such as field-programmable gate arrays, programmable logic arrays, systems-on-a-chip, systems-on-a-substrate, systems-on-package, application-specific integrated circuits, or any other reasonable means of integrating or packaging circuitry, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three implementation methods. Alternatively, at least one of the orbit type determination module 610, frequency difference analytical equation determination module 620, time difference analytical equation determination module 630, and clock difference compensation module 640 can be at least partially implemented as a computer program module, which can perform the corresponding function when the computer program module is run.

[0193] Figure 7 A block diagram schematically illustrates an electronic device suitable for implementing a spaceborne clock calibration method according to an embodiment of this application.

[0194] like Figure 7 As shown, an electronic device 700 according to an embodiment of this application includes a processor 701, which can perform various appropriate actions and processes according to a program stored in a read-only memory 702 or a program loaded from a storage portion 708 into a random access memory 703. The processor 701 may include, for example, a general-purpose microprocessor, an instruction set processor and / or an associated chipset and / or a dedicated microprocessor. The processor 701 may also include onboard memory for caching purposes. The processor 701 may include a single processing unit or multiple processing units for executing different steps of the method flow according to an embodiment of this application.

[0195] Random access memory 703 stores various programs and data required for the operation of electronic device 700. Processor 701, read-only memory 702, and random access memory 703 are interconnected via bus 704. Processor 701 executes various steps of the method flow according to embodiments of this application by executing programs in read-only memory 702 and / or random access memory 703. It should be noted that the programs may also be stored in one or more memories other than read-only memory 702 and random access memory 703. Processor 701 may also execute various steps of the method flow according to embodiments of this application by executing programs stored in said one or more memories.

[0196] According to embodiments of this application, the electronic device 700 may further include an input / output interface 705, which is also connected to a bus 704. The electronic device 700 may also include one or more of the following components connected to the input / output interface 705: an input section 706 including a keyboard, mouse, etc.; an output section 707 including a cathode ray tube, liquid crystal display, etc., and a speaker, etc.; a storage section 708 including a hard disk, etc.; and a communication section 709 including a network interface card, such as a local area network card, modem, etc. The communication section 709 performs communication processing via a network such as the Internet. A drive 710 is also connected to the input / output interface 705 as needed. A removable medium 711, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 710 as needed so that computer programs read from it can be installed into the storage section 708 as needed.

[0197] Embodiments of this application also provide a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs, which, when executed, implement the method according to the embodiments of this application.

[0198] According to embodiments of this application, the computer-readable storage medium can be a non-volatile computer-readable storage medium, such as including but not limited to: portable computer disks, hard disks, random access memory, read-only memory, erasable programmable read-only memory, portable compact disk read-only memory, optical storage devices, magnetic storage devices, or any suitable combination thereof. In embodiments of this application, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. For example, according to embodiments of this application, the computer-readable storage medium may include the read-only memory 702, and / or random access memory 703, and / or one or more memories other than read-only memory 702 and random access memory 703 described above.

[0199] Embodiments of this application also include a computer program product comprising a computer program containing program code for performing the methods shown in the flowchart. When the computer program product is run on a computer system, the program code is used to cause the computer system to implement the methods provided in the embodiments of this application.

[0200] In one embodiment, the computer program may rely on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may also be transmitted and distributed in the form of signals over a network medium, and may be downloaded and installed via the communication section 709, and / or installed from a removable medium 711. The program code contained in the computer program can be transmitted using any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination thereof.

[0201] In embodiments of this application, the computer program can be downloaded and installed from a network via communication section 709, and / or installed from removable medium 711. When the computer program is executed by processor 701, it performs the functions defined in the system of embodiments of this application. According to embodiments of this application, the systems, devices, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0202] According to embodiments of this application, program code for executing the computer programs provided in the embodiments of this application can be written in any combination of one or more programming languages. Specifically, these computational programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. The program code can be executed entirely on the user's computing device, partially on the user's device, partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0203] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0204] Those skilled in the art will understand that the features described in the various embodiments of this application can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this application. In particular, the features described in the various embodiments of this application can be combined and / or combined in various ways without departing from the spirit and teachings of this application. All such combinations and / or combinations fall within the scope of this application.

Claims

1. A method for calibrating a spaceborne clock, characterized in that, The method includes: Based on the orbital status information of the spacecraft to which the target satellite's onboard clock belongs, the orbital type of the spacecraft is determined, wherein the orbital type includes at least one of geocentric orbit, lunar orbit, and long-distance retrograde orbit; Based on the orbit type, the frequency difference analytical equation of the target satellite clock relative to Earth time is obtained. The frequency difference analytical equation includes a long-term frequency difference model and a periodic frequency difference model. The long-term frequency difference model is used to characterize the cumulative deviation of the satellite clock frequency over time, and the periodic frequency difference model is used to characterize the periodic fluctuation deviation of the satellite clock frequency. By integrating the frequency difference analytical equation, the time difference analytical equation of the target satellite clock relative to Earth time is obtained; Based on the time difference analytical equation, clock difference compensation is performed on the target satellite's onboard clock.

2. The method according to claim 1, characterized in that, In response to determining that the spacecraft's orbit type is a long-distance retrograde orbit, the step of obtaining the analytical equation for the frequency difference of the target satellite's clock relative to Earth time based on the orbit type includes: The single-point state of the spacecraft at a preset time on a long-distance retrograde orbit is obtained, and the single-point state includes a position vector and a velocity vector. Based on the single-point state, time-series state data within a preset time period is obtained, wherein the time-series state data includes position vectors and velocity vectors corresponding to multiple sampling times arranged in chronological order; Based on the time-series state data, determine the Jacobian constant at each sampling time and calculate the average value of the Jacobian constant within a preset time period. Based on the mean value of the Jacobian constant, the standard orbit corresponding to the spacecraft under the circularly restricted three-body problem is determined, and the standard time-series state data within the preset orbital period is obtained. Based on the standard time-series state data, harmonic coefficients were fitted to the velocities in the Earth-center distance, Moon-center distance, and Earth-Moon barycenter reference frame, respectively, to obtain multiple corresponding fitting models. Based on the fitted model, the analytical equation for the frequency difference of the target satellite clock relative to Earth time is determined.

3. The method according to claim 2, characterized in that, The method further includes: By superimposing a solar tidal compensation term into the frequency difference analytical equation, a modified frequency difference analytical equation is obtained. The solar tidal compensation term consists of a long-term constant frequency difference term and a frequency difference periodic term of the synodic lunar angular frequency.

4. The method according to claim 1, characterized in that, In response to determining that the spacecraft's orbit type is a geocentric orbit or a lunar orbit, the step of obtaining the analytical equation for the frequency difference of the target satellite clock relative to Earth time based on the orbit type includes: Based on the orbit type, obtain the orbital elements of the spacecraft in the centroid reference frame corresponding to the orbit type; Based on the orbital elements and the relativistic frequency shift relationship between coordinate time and Earth time in different centroid reference frames, the long-term frequency difference term model and the periodic frequency difference term model are obtained by decomposition. By combining the long-term frequency difference model and the periodic frequency difference model, the analytical equation for the frequency difference of the target satellite clock relative to Earth time is obtained.

5. The method according to claim 4, characterized in that, In response to determining that the spacecraft's orbit type is a lunar orbit, the long-term frequency difference model is obtained as follows: Based on the orbital elements, the first long-term term of frequency difference generated by the inherent time-direction lunar local coordinate time alignment of the target satellite clock is determined. The first long-term term of frequency difference is used to characterize the combined time delay effect of the second-order Doppler frequency shift and the non-spherical gravitational field of the moon on the spacecraft. Based on the average distance between the Earth and the Moon and the difference in gravitational potential between the Earth and the Moon, the second long-term term of frequency difference is determined when the local coordinates of the Moon are aligned with the coordinates of the Earth's center of mass. The second long-term term of frequency difference is used to characterize the frequency shift caused by the combined effect of the difference in gravitational potential energy and velocity between the Earth and the Moon in the Earth-Moon system. The third frequency difference long-term term generated by aligning the Earth's center-of-mass coordinates to Earth time is obtained. The third frequency difference long-term term is used to characterize the fixed reference offset between the Earth's center-of-mass coordinates and Earth time. Based on the average distance between the Sun and the Earth-Moon barycenter and the difference in gravitational potential between the Earth and the Moon, the long-term term of the solar tidal frequency difference caused by solar tidal perturbation is obtained; The first long-term frequency difference term, the second long-term frequency difference term, the third long-term frequency difference term, and the long-term frequency difference term of the solar tidal frequency difference term are combined to obtain the long-term frequency difference term model of the target satellite clock.

6. The method according to claim 5, characterized in that, In response to determining that the spacecraft's orbit type is a lunar orbit, the frequency difference periodic term model is obtained as follows: Based on the orbital elements, a general relativistic gravitational time delay model is obtained, and the first frequency difference long term is removed to separate the first frequency difference periodic term generated by the proper time alignment of the target satellite clock with the lunar local coordinates. The Earth-Moon time frequency difference model is obtained based on the difference in gravitational potential between the Earth and the Moon and the geocentric orbital elements of the Moon. The second frequency difference long-term term is removed to determine the second frequency difference periodic term generated when aligning the local coordinates of the Moon with the coordinates of the Earth's center of mass. The third frequency difference periodic term generated by aligning the Earth's center of mass coordinates to Earth time is obtained. The third frequency difference periodic term is used to characterize the periodic fluctuation deviation between the Earth's center of mass coordinates and Earth time. Based on the motion state vector of the lunar center in the Earth-Moon mass center reference frame and the motion state vector of the spacecraft in the lunar center reference frame, the non-inertial reference frame transformation coupling term is determined; A solar tidal torque model is obtained based on the gravitational parameters of the Sun, Earth, and Moon. The long-term solar tidal frequency deviation term is removed to separate the periodic solar tidal frequency deviation term. The frequency difference periodicity model of the target satellite clock is determined by combining the first frequency difference periodicity term, the second frequency difference periodicity term, the third frequency difference periodicity term, the non-inertial reference frame conversion coupling term, and the solar tidal frequency difference periodicity term.

7. The method according to claim 4, characterized in that, In response to determining that the spacecraft's orbit type is a geocentric orbit, the long-term frequency difference model is obtained as follows: Based on the orbital elements, the fourth long-term term of the frequency difference generated by the time alignment of the target satellite clock with the Earth's center of mass coordinates is determined. The fourth long-term term of the frequency difference is used to characterize the combined time delay effect of the second-order Doppler frequency shift and the Earth's non-spherical gravitational field on the spacecraft. The fifth frequency difference long-term term generated by aligning the Earth's center-of-mass coordinates to Earth time is obtained. The fifth frequency difference long-term term is used to characterize the fixed reference offset between the Earth's center-of-mass coordinates and Earth time. The fourth and fifth long-term frequency difference terms are combined to obtain the long-term frequency difference term model of the target satellite clock.

8. The method according to claim 7, characterized in that, In response to determining that the spacecraft's orbit type is a geocentric orbit, the frequency difference periodic term model is obtained as follows: Based on the orbital elements, a general relativistic gravitational time delay model is obtained, and the fourth frequency difference long term is removed to separate the fourth frequency difference periodic term generated by the time alignment of the target spacecraft's onboard clock with the Earth's center of mass coordinates. The general relativistic gravitational time delay model is used to characterize the combined time delay effect of gravitational potential, velocity, and Earth's non-spherical gravitational field on the spacecraft. The fifth frequency difference periodic term generated when aligning the Earth's center of mass coordinates to Earth time is used to characterize the periodic fluctuation deviation between the Earth's center of mass coordinates and Earth time. The fourth frequency difference period term is combined with the fifth frequency difference period term to obtain the frequency difference period term model of the target satellite clock.

9. The method according to claim 4, characterized in that, The orbital elements used in the frequency difference periodic term model are the instantaneous orbital elements.

10. A spaceborne clock calibration device, characterized in that, The device includes: The orbit type determination module is used to determine the orbit type of the spacecraft based on the orbital state information of the spacecraft to which the target satellite clock belongs. The orbit type includes at least one of geocentric orbit, lunar orbit, and long-distance retrograde orbit. The frequency difference analytical equation determination module is used to obtain the frequency difference analytical equation of the target satellite clock relative to Earth time according to the orbit type. The frequency difference analytical equation includes a long-term frequency difference model and a periodic frequency difference model. The long-term frequency difference model is used to characterize the cumulative deviation of the satellite clock frequency over time, and the periodic frequency difference model is used to characterize the periodic fluctuation deviation of the satellite clock frequency. The time difference analytical equation determination module is used to perform integral operations on the frequency difference analytical equation to obtain the time difference analytical equation of the target satellite clock relative to Earth time; and The clock error compensation module is used to compensate for the clock error of the target satellite clock based on the time difference analytical equation.

Images